Ivan Andrus (CEU): Some dualities between conjugacy classes and irreducible characters

Abstract: Robinson has shown that the character degrees are determined by knowing, for all n, the number of ways that the identity can be expressed as a product of n commutators. Earlier, Strunkov showed that the existence of characters of p-defect 0 can be determined by counting solutions to certain equations involving commutators and conjugates.

In this paper, we prove analogs to Robinson's and Strunkov's theorems by switching conjugacy classes and characters. We show that counting the multiplicity of the trivial character in certain products of characters determines the conjugacy class sizes and existence of conjugacy classes with p-defect 0.